Following our general principle, we would naturally tend to choose the negative log-likelihood function of the cluster-averages \((\bar{}_1,...,\bar{}_n)\)  as the empirical risk function \(Q_n()\)  in (REF ). Along this line, [1]} proposed the de-biased estimator for Gaussian graphical models. However, the inference requires the irrepresentable condition [2]} on \(^*\) , which can be restrictive. The alternative methods proposed by [3]}, [4]} imposed the condition that the largest eigenvalue of \(^*\)  is bounded. These technical conditions on \(^*\)  are difficult to justify and can be avoided by using our approach. We propose to estimate each sparse row of \(^*\)  as explained below.
